Elementary Algebra

Toby Wagner

• Publisher: Chemeketa Press
• Year: 2021
• ISBN:
  9781943536894
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Elementary Algebra provides precollege algebra students with the essentials for understanding what algebra is, how it works, and why it so useful. It is written with plain language and includes annotated examples and practice exercises so that even students with an aversion to math will understand these ideas and learn how to apply them. This textbook expands on algebraic concepts that students need to progress with mathematics at the college level, including linear models and equations, polynomials, and quadratic equations. Written by faculty at Chemeketa Community College for the students in the classroom, Elementary Algebra is a classroom-tested textbook that sets students up for success.

CHAPTER 1

Solving Linear Equations and Inequalities

Solving equations is at the heart of algebra. Because of this, it seems fitting to begin our study of elementary algebra by learning how to solve equations algebraically. In Chapter 1, we will focus on solving linear equations, which are typically less complicated than non-linear equations. We will also learn how to solve linear inequalities. As we progress through the chapter, we will be using our skills to help us solve application problems, which are commonly known as “word problems” or “story problems.”

In this chapter, you’ll study the following topics:

1.1 Solving Linear Equations

1.2 Solving Multi-Step Equations

1.3 Solving Literal Equations

1.4 Solving Linear Inequalities

1.1 Solving Linear Equations

Overview

Here’s a problem:

The area of a rectangle is the same as the value found by multiplying the length and the width. A rectangle that is 14 feet long has an area of 91 square feet. What is the width of the rectangle?

This problem states that two things are the same — the area of the rectangle and the value found by multiplying the length and width. Mathematicians write many sentences like this, though usually with mathematical notation instead of words. In math, equations are used to communicate sameness. Equations are the most common sentences in math.

When you are finished with this section, you will be able to:

◆ Identify various types of equations

◆ Understand the meaning of solutions and equivalent equations

◆ Use addition and subtraction to solve 1-step equations

◆ Use multiplication and division to solve 1-step equations

◆ Solve application problems involving 1-step equations

At the end of this section, we will write and solve an equation to find the width of the rectangle in the problem above. In the meantime, let’s learn more about equations.

A. Types of Equations

An equation is a mathematical sentence that asserts that two things are the same or equal. An equals sign (=) means “is the same as.” It’s important, though, to understand that an equation only asserts that two things are the same. As you’ll soon see, this doesn’t guarantee that the statement is actually true.

Some equations are always true. These equations are called identities. Identities are equations that are true for all acceptable values of the variable. Here are some examples of identities:

5x = 5x	is true for all acceptable values of x because 5 times any number is always the same as 5 times that same number.
y + 1 = y + 1	is true for all acceptable values of y because any number plus 1 is...